Optimization of Thermodynamic Efficiency vs. Capacity for a Communications Systems

ABSTRACT

The present disclosure relates to the modeling of communications systems using information theory and thermodynamic principles. The disclosure establishes a fundamental relationship between thermodynamic efficiency and capacity for communications systems based on fundamental physical principles, applicable to communications processes. Further, principles of efficiency optimization with an emphasis on electronic communications platforms are introduced herein.

CROSS REFERENCE TO RELATED APPLICATIONS

This application claims the benefit of U.S. Provisional Patent Application No. 61/975,077 (Atty. Docket No. 1744.2390000), filed Apr. 4, 2014, titled “Thermodynamic Efficiency vs. Capacity for a Communications System,” U.S. Provisional Application No. 62/016,944 (Atty. Docket No. 1744.2410000), filed Jun. 25, 2014, titled “Momentum Transfer Communication,” and U.S. Provisional Application No. 62/115,911 (Atty. Docket No. 1744.2420000), filed Feb. 13, 2015, titled “Optimization of Thermodynamic Efficiency Versus Capacity for Communications Systems,” all of which are incorporated herein by reference in their entireties.

SUMMARY

In contrast to conventional “ad hoc” approaches, optimum momentum transfer simultaneously maximizes power efficiency and information transfer. Therefore, the maximum information per unit of energy resource is transferred through communication functions or communications system and channel using momentum transfer techniques. Hence, battery requirements for mobile devices may be reduced or battery life extended. Also, heat dissipation within a communications device may be minimized. Moreover, the momentum transfer technique provides a unified theoretical optimization approach superior to current design approaches. Resulting architectures are more efficient for lower investment of energy and hardware.

Although there are practical limitations, momentum transfer optimization techniques predict asymptotic efficiency limits of 100% for select architectures. The efficiency limits may be traded for reduced architecture complexity in a systematic may using parameters of optimization which are tied to the architecture at a fundamental level. Hence, the maximum performance may be obtained for the minimum hardware investment using the disclosed strategies.

Momentum transfer techniques apply to any communications process technology whether electrical, mechanical, optical, acoustical, chemical or hybrid. It is a desirable technique for the ever decreasing geometries of communication devices and well suited for optimization of nana-scale electro-mechanical technologies. Momentum transfer may be theoretically expressed in a classical or quantum mechanical context since the concept of momentum survives the transition between the regimes. This includes relativistic domains as well.

The fundamentals of the momentum transfer theory are subject to the laws of motion whether classical, relativistic or quantum. All communication process are composed of the interactions of particles and/or waves at the most fundamental level. We on occasion refer to these structures as virtual particles as well. The motions and interactions are described by vectors and each virtual particle exchange vector quantities in a communications event. These exchanged vector quantities governed by physical laws are best characterized as momentum exchanges. The nature of each exchange determines how much information is transferred and the energy overhead of the exchange. It is theoretically possible to maximize the transferred information per exchange while minimizing the energy overhead.

A simple billiards example illustrates some relevant analogous concepts. We consider the interaction of the billiards balls to be analogous to the interaction of particles, waves and virtual particles within a communications process. Suppose the cue ball strikes a target ball head on. If the cue ball stops so that its motion is arrested at the point of impact, and the target ball moves with the original cue ball velocity after impact, then all the momentum of the cue ball has been transferred to the targeted ball, imparting momentum magnitude and deflected angle, in this case zero degrees as an example. Now suppose that an angle other than zero degrees is desired as a deflection angle with a momentum magnitude transferred in the target ball equivalent to the first interaction example. The cue ball must strike the target ball at a glancing angle to impart a recoil angle other than zero. Both the cue ball and target ball will be in relative motion after the strike. Thus, the transferred momentum is proportional to the original cue ball momentum magnitude divided by the cosine of glancing angle. The deflection angle for the target ball is equal to the glancing angle mirrored about an axis of symmetry determined by the prestrike cue ball trajectory. It is easy to reckon that the cue ball must move at increasing velocities to create a desired target ball speed as the glancing angle becomes more extreme. For instance, a glancing angle of 0° is very efficient and a glancing angle of nearly 90° results in relatively small momentum transfer. It should be apparent that the billiard example represents particle interaction at a fundamental scale and could be applied to a bulk of electrons, photons and other types of particles or waves where the virtual particles carry encoded information in a communications apparatus. The various internal processing functions of the apparatus will possess some momentum exchange between these particles at significant internal interfaces of a relevant model. This prior billiard example has ignored any internal heat losses or collision imperfections of the billiard exchange assuming perfect elasticity. In reality there are losses due to imperfections and the 2^(nd) Law of Thermodynamics.

The conceptual essence of the prior example can apply to the waving of a signal flag, beating of a drum and associated acoustics, waveforms created by the motions of charged particles like electrons or holes, or visual exchanges of photons which in turn could stimulate electrochemical signals in the brain.

Large peak to average power ratio (PAPR) waveforms are capable of transferring greater amounts of information compared to waveforms of lower peak to average power (PAPR) provided the probability density of the appropriate waveform variable is adequate. In general, Shannon's information measure is the metric to determine the relative information transfer capacities. A large dynamic range for PAPR is analogous to a very wide range of glancing or strike angles in the billiards example as well as an accompanying wide range of target ball momentum magnitudes. The more random the angles and magnitudes the greater the potential information transfer in an analogous sense. However, when the momentum of each interaction of a communications process is not completely transferred at a fundamental level then energy is wasted. Only the analogous “head on” collisions at zero degrees effective angle transfer energy at a 100% efficiency.

If one restricts the interactions to “head on” then the randomness of the momentum exchange angle and magnitude are reduced, thereby asymptotically reducing encoded information in the relative motions to zero. The disclosed momentum transfer technique provides a method to overcome this impasse so that the diversity of momentum exchanges can be preserved while maximizing efficiency, thereby maintaining capacity.

An extended billiards analogy helps illustrate an optimization philosophy. In the original illustration the relative positions and velocities of the cue and target halls are restricted in a certain manner. That is, certain game rules are assumed. Suppose however, that the rules are modified so that for each shot (billiard exchange) we may spot the cue ball to a location such that the motion of the target ball after an exchange is exactly in the desired direction and the striking angle is “head on”. If we further permit the velocity of the cue ball or more appropriately the momentum magnitude to assume the desired value then each and every exchange can be 100% effective and efficient. This requires complete degree of freedom for cue ball spotting and cue ball velocity given a particular cue ball mass. Now if we do not have complete freedom to place the cue ball but perhaps we have the ability to locate the cue ball with a resolution of say 36° relative to some reference position associated with the target ball then the maximum overhead in the required momentum magnitude is approximately limited to no greater than 23.6%. This is proportional to approximately 94.4% efficiency. Thus, reduction of infinite precision of the cue ball spotting (which corresponds to 100% efficiency), to 10 zones of angular domains of 36° about the target, results in an efficiency loss of roughly only 5.6%. Similarly, the number of degrees of freedom in a modulator or demodulator, encoder or decoder, or other communications function may be traded for efficiency. The enhanced degrees of freedom permit more control of the fundamental particle exchanges which underlie the communications process thereby, selecting the most favorable effective angles of momentum exchange on the average, albeit these angles may be in a hyperspace geometry rather than a simple 2-D geometry as indicated in the billiards example.

It turns out however these degrees of freedom are not arbitrarily partitioned within their respective and applicable domains. For instance, the prior example of 10 36° equi-partitioned zones, while good, may not be optimal for all scenarios. Optimization is dependent on the nature of the statistics governing the random communications process conveyed by the function to be optimized. Optimized Momentum Transfer Theory provides for the consideration of the relevant communications process statistic. Momentum transfer is unique amongst optimization theories because it provides a direct means of obtaining the calculation and specification of partitions which are optimal. Once again, returning to the billiards example, momentum transfer theory would determine out of 10 angular partitions the optimal span and relative location of each angular partition domain, depending on probability models associated with the target ball trajectories vs. the thermodynamic efficiency of each trajectory. Over the course of a game and many random momentum exchanges the momentum transfer approach would guarantee the minimum energy expenditure to play the game, given some finite resolution of cue ball spotting placement.

Further features and advantages of the embodiments disclosed herein, as well as the structure and operation of various embodiments, are described in detail below with reference to the accompanying drawings. It is noted that the invention is not limited to the specific embodiments described herein. Such embodiments are presented herein for illustrative purposes only. Additional embodiments will be apparent to a person skilled in the relevant art based on the teachings contained herein.

LISTING OF EXHIBITS

Embodiments of the present invention are disclosed in the following exhibits (attached hereto and forming a part of this application):

-   -   1. Exhibit A:“Thermodynamic Efficiency vs. Capacity for a         Communications System,” U.S. Provisional Patent Application No.         61/975,077 (Atty. Docket No. 1744.2390000), filed Apr. 4, 2014;     -   2. Exhibit B: “Momentum Transfer Communication,” U.S.         Provisional Application No. 62/016,944 (Atty. Docket No.         1744.2410000), filed Jun. 25, 2014;     -   3. Exhibit C: “Optimization of Thermodynamic Efficiency Versus         Capacity for Communications Systems,” U.S. Provisional         Application No. 62/115,911 (Atty. Docket No. 1744.2420000),         filed Feb. 13, 2015, titled; and     -   4. Exhibit D: “An Optimization of Thermodynamic Efficiency vs.         Capacity for Communications Systems,” Ph.D. Dissertation of         Gregory S. Rawlins, University of Central Florida, 2015.

It is to be appreciated that the disclosures in the attached exhibits and not the Summary and Abstract sections, is intended to be used to interpret the claims. The Summary and Abstract sections may set forth one or more but not all example embodiments of the present invention as contemplated by the inventors and thus are not intended to limit the present invention and the appended claims in any way.

Embodiments of the present invention have been described above with the aid of functional building blocks illustrating the implementation of specified functions and relationships thereof. The boundaries of these functional building blocks have been arbitrarily defined herein for the convenience of the description. Alternate boundaries can be defined so long as the specified functions and relationships thereof are appropriately performed.

The foregoing description of the specific embodiments will so fully reveal the general nature of the invention that others can, by applying knowledge within the skill of the relevant art, readily modify and/or adapt for various applications such specific embodiments, without undue experimentation, without departing from the general concept of the present invention. Therefore, such adaptations and modifications are intended to be within the meaning and range of equivalents of the disclosed embodiments, based on the teaching and guidance presented herein. It is to he understood that the phraseology or terminology herein is for the purpose of description and not of limitation, such that the terminology or phraseology of the present specification is to be interpreted by a person skilled in the relevant art in light of the teachings and guidance.

The breadth and scope of the present invention should not he limited by any of the above-described example embodiments, but should be defined only in accordance with the following claims and their equivalents. 

What is claimed is:
 1. A method for modeling a communications system, the method comprising: determining a capacity for the communications system in the communications system; associating the capacity with one or more thermodynamic efficiencies to generate one or more efficiency optimizations; and applying the one or more efficiency optimizations to the communications system. 